E3P51D
Demonstration — Part III
Latin
Corpus humanum (per postulatum 3 partis II) a corporibus externis plurimis modis afficitur. Possunt igitur eodem tempore duo homines diversimode esse affecti atque adeo (per axioma 1 quod est post lemma 3, quod vide post propositionem 13 partis II) ab uno eodemque objecto possunt diversimode affici. Deinde (per idem postulatum) corpus humanum potest jam hoc jam alio modo esse affectum et consequenter (per idem axioma) ab uno eodemque objecto diversis temporibus diversimode affici. Q.E.D.
English (Elwes 1883)
The human body is affected by external bodies in a variety of ways (II. Post. iii.). Two men may therefore be differently affected at the same time, and therefore (by Ax. i. after Lemma iii. after II. xiii.) may be differently affected by one and the same object. Further (by the same Post.) the human body can be affected sometimes in one way, sometimes in another; consequently (by the same Axiom) it may be differently affected at different times by one and the same object. Q.E.D.
Modern English
The human body can be affected by external bodies in a great many ways (E2Post3). Two people can therefore be differently affected at the same time, and so (E2A1) can be differently affected by one and the same object. Further, by the same Postulate (E2Post3), the human body can at one time be affected in one way and at another time in another way, and consequently (E2A1) it can be differently affected at different times by one and the same object. Q.E.D.